Estimating adsorption isotherm parameters in chromatography via a virtual injection promoting double feed-forward neural network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve a nonlinear inverse problem in a partial differential equation so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the uniqueness of adsorption isotherms cannot be guaranteed, and moreover, the small noise in the measured response can lead to a large fluctuation in the traditional estimation of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method-the virtual injection promoting double feed-forward neural network (VIP-DFNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model-a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-DFNN is an efficient and robust algorithm.